| Abstract: |
| The cubic nonlinear Schr\odinger equation (NLS) arises as a model for the propagation of intense continuous wave
laser beams in a homogeneous medium. In practice, it has also been successful in modeling optical experiments
in inhomogeneous settings. This suggests the occurrence of homogenization, that is, in a large scale limit,
solutions to the inhomogeneous equation converge to the solution of a homogeneous NLS. We will review some
recent homogenization results for physically motivated examples. While materials with a periodic structure are the most natural setting to consider this problem, our examples include a model where strong defects are sprinkled randomly across the medium. Part of this talk is based on joint work with B. Harrop-Griffiths. |
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